We have continued to employ the concepts of Mandelbrot's fractal geometry to the quantitative studies of central nervous system neurons, and other cell types grown in tissue culture or from whole animals. We do this by employing image processing techniques to measure the fractal dimension (D), which is a measure of the complexity of the structure under investigation. In particular, the D relates to the degree of branching (e.g., of dendrites), the ruggedness of borders and the degree of space- filling of the object of interest. We have undertaken, in separate studies, how the fractal dimension changes during the differentiation and growth of glial cells from different sources (optic nerve and brain) and of neurons in tissue culture. We have found that both optic nerve and brain-derived oligodendrocytes differentiate faster and to a greater extent than do both types of astrocytes, and that nerve-derived glia also differentiate faster and to a greater extent than do brain-derived glia. Interestingly, the rates of differentiation, as measured by D, can be described by a single time constant. The work on cultured spinal neurons shows that the cells can be classified into four groups on the basis of the number of their primary dendrites and that they differentiate in a similarly simple fashion, with each of the four groups having distinctive final D values and time constants. We have proposed that D is a useful, quantitative and unbiased measure of morphological differentiation. We examined the Ds of cerebellar Purkinje cells from nine vertebrate species, ranging from birds through marsupials to mammals, including man. This indicates a phylogenetic constancy of Purkinje cell morphological complexity going back at least as far as birds in the evolutionary tree. We have begun studies of the development of the internal and surface structures of cultured rat hippocampal neurons with fluorescence and confocal microscopy in order to localize the position of GABA and glutamate boutons. We find that GABA boutons are located almost exclusively on somata and proximal dendrites, while glutamate boutons are mainly on peripheral dendrites but occasionally on proximal dendrites and less so on somata. We continue in our efforts to improve the performance of our confocal microscope with no moving parts by changes in design and components.